Articles | Volume 17, issue 1
Nonlin. Processes Geophys., 17, 49–63, 2010
https://doi.org/10.5194/npg-17-49-2010

Special issue: Nonlinear processes in oceanic and atmospheric flows

Nonlin. Processes Geophys., 17, 49–63, 2010
https://doi.org/10.5194/npg-17-49-2010

  02 Feb 2010

02 Feb 2010

A study of the phase instability of quasi-geostrophic Rossby waves on the infinite β-plane to zonal flow perturbations

L. Marié L. Marié
  • Laboratoire de Physique des Océans, UMR6523 CNRS/IFREMER/IRD/UBO, IFREMER/Centre de Brest, 29280 Plouzané, France

Abstract. The problem of the linear instability of quasi-geostrophic Rossby waves to zonal flow perturbations is investigated on an infinite β-plane using a phase dynamics formalism. Equations governing the coupled evolutions of a zonal velocity perturbation and phase and amplitude perturbations of a finite-amplitude wave are obtained. The analysis is valid in the limit of infinitesimal, zonally invariant perturbation components, varying slowly in the meridional direction and with respect to time. In the case of a slow sinusoidal meridional variation of the perturbation components, analytical expressions for the perturbation growth rates are obtained, which are checked against numerical codes based on standard Floquet theory.